Subgroups — C₃×C₃⋊D₃ #277

Order 54.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊D₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₃	—	3	4	no	maximal
4	C₃²	—	2	4	no	—
5	C₃²	D₃	1	4	yes	complemented
6	C₃²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃	—	9	1	no	—
8	D₃	—	3	4	no	—
9	C₃	—	2	4	no	—
10	C₃	C₃×D₃	1	4	yes	complemented
11	C₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
12	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃³	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₃

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.